In Exercises 9-12, which of the given subsets of C[1,1] are subspaces of C[-1, 1]? 9. F = {f(x) in C[−1, 1]: ƒ(−1) = −ƒ(1)} 10. F = {ƒ (x) in C[−1, 1]: ƒ(x) ≥ 0 for all x in [−1,1]} 11. F = {f(x) in C[−1, 1]: ƒ(−1) = −2 and f(1) = 2} 12. F = {f(x) in C[-1, 1]: f(1/2) = 0}
In Exercises 9-12, which of the given subsets of C[1,1] are subspaces of C[-1, 1]? 9. F = {f(x) in C[−1, 1]: ƒ(−1) = −ƒ(1)} 10. F = {ƒ (x) in C[−1, 1]: ƒ(x) ≥ 0 for all x in [−1,1]} 11. F = {f(x) in C[−1, 1]: ƒ(−1) = −2 and f(1) = 2} 12. F = {f(x) in C[-1, 1]: f(1/2) = 0}
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![In Exercises 9-12, which of the given subsets of
C[1,1] are subspaces of C[-1, 1]?
9. F = {f(x) in C[−1, 1]: ƒ(−1) = −ƒ(1)}
10. F = {f(x) in C[−1, 1]: f(x) ≥ 0 for all x in
[−1,1]}
11. F = {f(x) in C[−1, 1]: ƒ(−1) = −2 and
f(1) = 2}
12. F = {f(x) in C[-1, 1]: f(1/2) = 0}](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4fb02365-efda-4f71-9185-5332218a7cc4%2F1dbae5be-6786-4889-88a9-96470fe8d8b9%2F2xtvfgl_processed.png&w=3840&q=75)
Transcribed Image Text:In Exercises 9-12, which of the given subsets of
C[1,1] are subspaces of C[-1, 1]?
9. F = {f(x) in C[−1, 1]: ƒ(−1) = −ƒ(1)}
10. F = {f(x) in C[−1, 1]: f(x) ≥ 0 for all x in
[−1,1]}
11. F = {f(x) in C[−1, 1]: ƒ(−1) = −2 and
f(1) = 2}
12. F = {f(x) in C[-1, 1]: f(1/2) = 0}
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